Question

The neck and bottom of a bottle are $3cm$ and $15cm$ in radius respectively. If the cork is pressed with a force $12N$ in the neck of the bottle, then force exerted on the bottom of the bottle is

• A. $30N$
• B. $150N$
• C. $300N$
• D. $600N$

Answer 1

Answer: (C)

Pressure at neck of bottle
$p_1=\frac{F_1}{A_1}=\frac{F_1}{\pi r_1^2}$
Similarly, pressure at bottom of bottle
$p_2=\frac{F_2}{A_2}=\frac{F_2}{\pi r_2^2}$
According to Pascal's law, liquids transmits pressure equal in all directions.
$\therefore$ $\frac{F_2}{A_2}=\frac{F_2}{{\left(\pi r\right)}_2^2}or{F}_2=F_1\times {\left(\frac{r_2}{r_1}\right)}^2$
$=12\times {\left(\frac{15}{3}\right)}^2=12\times 25=300N$